Question

Three objects, $A$ : (a solid sphere), $B$ : (a thin circular disk) and $C$ : (a circular ring), each have the same mass $M$ and radius $R$. They all spin with the same angular speed to about their own symmetry axes. The amounts of work $(W)$ required to bring them to rest, would satisfy the relation

• A. $W_A > W_C > W_B$
• B. $W_C > W_B > W_A$
• C. $W_B > W_A > W_C$
• D. $W_A > W_B > W_C$

Answer 1

Answer: (B)

$W_C > W_B > W_A$

Answer 2

Work done required to bring them rest $\Delta W = \Delta KE$ $\Delta W = \frac{1}{2}I\omega^{2}$ $\Delta W \propto I$ for same $\omega$ $W_{A } : W_{B} : W_{C} = \frac{2}{5} MR^{2} : \frac{1}{2} MR^{2} : MR^{2}$ $= \frac{2}{5} : \frac{1}{2} : 1$ $= 4 : 5 : 10$ $\Rightarrow W_{C} > W_{B } > W_{A}$